The sport known for its "saddle" riding contests is equestrian sports, particularly in events like dressage and show jumping. In these competitions, riders perform intricate maneuvers with their horses while mounted in a saddle, displaying skill, control, and harmony between horse and rider. Equestrian competitions can also include eventing, which combines dressage, cross-country, and show jumping in one event. These contests require rigorous training for both horse and rider to excel in various disciplines involved, showcasing a unique blend of athleticism, strategy, and artistry.